Question

find the value of k , for which the quadratic equation 2x²+3x+k=0 has equal roots​

Answer 1

EXPLANATION.

→ Quadratic equation → 2x² + 3x + k = 0

has equal roots.

→ To find value of k.

→ For equal roots = D = 0 or b² - 4ac = 0.

→ (3)² - 4(2)(k) = 0

→ 9 - 8k = 0

→ 9 = 8k

→ k = 9/8.

→ More information.

→ D = 0 or [ b² - 4ac = 0 ]

roots are real and equal.

→ D > 0 or [ b² - 4ac > 0 ]

roots are real and unequal.

→ D < 0 or [ b² - 4ac < 0 ]

roots are imaginary.

Answer 2

Answer:

Given :-

• The quadratic equation is 2x² + 3x + k = 0 has equal roots.

To Find :-

• What is the value of k.

Solution :-

Given equation :-

$\mapsto$ 2x² + 3x + k = 0

where, a = 2, b = 3, c = k

$\leadsto$ The two roots are real and equal.

➣ Discriminant = 0

➨b² - 4ac = 0

⇒(3)² - 4(2)(k) = 0

⇒9 - 8k = 0

⇒- 8k = -9

➠ k = $\dfrac{9}{8}$

$\therefore$ The value of k is $\dfrac{9}{8}$

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✪ Extra Information ✪

❖ The two roots of qradratic equation are ax² + bx + c = 0

⊛ Real and equal if b² - 4ac = 0

⊛ Real and unequal if b² - 4ac > 0

⊛ No real roots if b² - 4ac < 0

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